SEMINAR: Groups and Combinatorics Seminar, On the number of matroids

Abstract:

Matroids are combinatorial structures that generalize graphs as well as configurations of points in projective space. They consist of a finite ground set E and a set of subsets of E called B, such that B satisfies certain axioms. We consider the problem of bounding the number m_n of matroids on a fixed ground set of size n. In 1973, Piff showed that log log m_n < n- log n + O(log log n) In 1974, Knuth gave a lower bound of log log m_n > n- (3/2) log n + (1/2) log(2/pi) - o(1) In the talk, I will present a recent result with Nikhil Bansal and Jorn van der Pol, that log log m_n < n- (3/2) log n + (1/2) log(2/pi) + 1 + o(1)